Quantitative measure for the spin-charge separation in two dimensional Hubbard model

We introduce a qauantitative measure of spin-charge separation, $ζ(t)$ which is based on the difference between the fluctuations with respect to background of the spin and charge profiles at any time t and is suitable for studying the non-equilibrium dynamics of excitations in strongly correlated systems. This quantity is not only a direct measure of the spin-charge separation in strongly correlated systems, but its long time behaviour can further serve as a possible order parameter for the interaction induced (Mott) insulating state. Within the nu- merically exact diagonzalization we calculate this quantity for the two dimensional Hubbard model away from Half filling. Our quantitative measure in chain, ladder and two-dimensional geometries gives the same order of magnitude for the quantity of spin-charge separation. Furthermore from the temporal behaviour of $ζ(t)$ a threshold time can be identified that provides clues onto the breakdown of underlying Mott insulating phase.

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